Question

1. Metallic strontium crystallizes in a face-centered cubic lattice, with one Sr atom per lattice point. If the edge length of the unit cell is found to be 608 pm, what is the metallic radius of Sr in pm?
2. The substance beta manganese is found to crystallize in a cubic lattice, with an edge length of 630.0 pm. If the density of solid beta manganese is 7.297 g/cm3, how many Mn atoms are there per unit cell?

Answer 1

Answer:

$r=215pm$

$N_{Mn}=20$

Explanation:

From the question we are told that:

Edge length of the unit cell $l=608pm$

a)

Generally the equation for The relationship between edge length and radius is mathematically given by

$4r=\sqrt{2a}$

Therefore

$4r=\sqrt{2*608}$

$r=\frac{\sqrt{2*608}}{4}$

$r=215pm$

b)

From the question we are told that:

Density $\rho=7.297$

Edge length of $l=630.0 pm=>630*10^-{10}$

Therefore Volume  is given as

$V=l^3$

$V=630*10^-{10}^3$

$V=2.50047*10^{−22}$

Generally the equation for Mass is mathematically given by

$m=Volume*density$

$m=V*\rho$

$m=2.50047*10^{−22}*7.297$

$m=1.83*10^{-21}g$

Therefore Molarity is given as

$n=\frac{M}{Molar M}$

$n=\frac{1.83*10^{-21}g}{55}$

$n=3.32*10^{-23}$

Finally The atoms in a unit cell is

$N_{Mn}=Moles*Avogadro\ constant$

$N_{Mn}=3.32*10^{-23}*6.023*10^{23}$

$N_{Mn}=20$